A358881 a(n) is the smallest prime p such that p^2 - 1 has 2*n divisors, or -1 if no such prime exists.

2, 3, -1, 5, 7, -1, -1, 11, 17, 23, -1, 19, -1, 31, 73, 29, -1, 383, -1, 41, 97, -1, -1, 79, -1, -1, 127, 223, -1, 71, -1, 109, -1, -1, 2593, 197, -1, -1, -1, 281, -1, 1439, -1, 34303, 199, -1, -1, 181, -1, 647, -1, 6143, -1, 7057, -1, 929, -1, -1, -1, 521, -1

Offset: 1

Author

Jon E. Schoenfield, Dec 04 2022

Keywords

• sign
• hard

Comments

See A350780 for a discussion about the prime solution to d(p^2 - 1) = 2*n for n in certain cases. - Jianing Song, Feb 15 2025

Examples

			For p = 11, p^2 - 1 = 121 - 1 = 120 = 2^3 * 3 * 5 has 16 divisors. 11 is the smallest prime p such that p^2 - 1 has 16 = 2*8 divisors, so a(8) = 11.
There does not exist any prime p such that p^2 - 1 has 6 = 2*3 divisors, so a(3) = -1.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..374
• Jianing Song, Notes on A350780 and A358881 (1)
• Jianing Song, Notes on A350780 and A358881 (2)
• Jianing Song, PARI program for A350780 and A358881

Crossrefs

Cf. A000005, A000040, A341655, A341658, A341660, A350780.

Programs

PARI

\\ See Links. Jianing Song, Feb 16 2025